UNIT 1 2017 Flashcards
what is the shortcut normcdf?
gives % from raw data, skips Z score. normcdf (low VALUE, high VALUE, mean, sd)
what is the shortcut invnorm?
gives data value from percentile, skips Z score. Invnorm (percentile, mean, sd)
Why do we plug 999 into normcdf?
It needs a z score, but we can’t plug in infinity. So we go down or up 999 standard deviations and that pretty much gets everything
If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them, and one of them had 9 pickles, then the number 9 from that burger would be called ____?
a datum, or a data value.
What is data?
Any collected information. Generally each little measurement, Like, if it is a survey about liking porridg, the data might be ?yes, yes, no, yes, yes? if it is the number of saltines someone can eat in 30 seconds, the data might be ?3, 1, 2, 1, 4,3 , 3, 4?
If you want to find percentile for a value, what do you put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright) like going from negative infinity up to the z score
are there any normal samples?
no, nothing is normal, just normalish. The only normal thing is the model we use.
How can you describe spread?
range, IQR, stand dev, variance, or simply say: From here, to about here
How can you think about the mean and median to remember the difference when looking at a histogram?
mean is balancing point of histogram, median splits the area of the histogram in half.
Compare DATA-STATISTIC-PARAMETER using CATEGORICAL example
Data are individual measures? like meal preference: ?taco, taco, pasta, taco, burger, burger, taco? Statistics and Parameters are summaries. A statistic would be ?42% of sample preferred tacos? and a parameter would be ?42% of population preferred tacos.? Notice that for categorical variables, the categories are words and the statistics and parameters are percents.
Give a simple example showing that adding a constant doesn’t change the spread, but changes the center. (this always happens)
Data set: 1,2,3,4,5 Spread (range):4, Center: 3
add three and get new data set: 3,4,5,6,7 spread:4 Center: 5 (center went up, spread stayed the same). The IQR and SD will stay the same, but median and mean go up 3. Called shifting, or sliding the data.
what is a nice mean/median/mode helper diagram?
Sketch a skewed left distribution, then mean/median/mode will be labeled in order from L to R
data or datum?
datum is singular, Like “hey dude, come see this datum I got from this rat!” data is the plural, “hey look at all that data Edgar got from his brussel sprouts”
If a distribution is skewed left, what will be greater, the mean or median? WHY?
Median. The mean moves left to keep balance.
When drawing a graph or chart, what do you have to remember to do?
LABEL AXES, make a KEY(if needed ) AND GIVE IT A NAME!!! “Figure 1: Age and Food Preference”
What is the difference between a bar chart and a histogram
bar charts are for categorical data (bars don’t touch and can often be in any order) and histograms are for quantitative data (bars usually touch and x axis is in order)
What is a quantitative variable? Compared to quantitative data?
Quantitative variable are the things your are interested in like: Height, age, price, number of cars sold, SAT score. Quantitative data are the actual heights or ages from individuals: 54” , 2 years, $ 34.99
Why don’t we just use the average (mean) all the time? (instead of mode and median)
The word average is a general term that can be actually talking about the mean, median or mode. We don’t always use the mean because it is not RESILIENT, it is impacted by skewness and outliers
How can you tell if variables in a contingency table are independent?
If the distributions are the same across the variables.. Then it doesn’t DEPEND? so INDEPENDENT. Ex: 30% of freshman and 30% of seniors like cabbage.
What is a categorical variable? Compare to categorical data.
Categorical (or qualitative) variables are the categories you are interested in like “hair color” and “music preference”. The data are the measureds from individuals like: SUV, sedan, Listens to Hip Hop, Female, yes, no, etc.
When are box plots used most often?
When comparing a bunch of different sets of data.
How do you describe distributions (histograms)?
Shape-Cener-Spread- and STRANGE (Outliers and gaps) some say GSOCS. where’s yo GSOCS?
what happens if you multiply all of a data set by a constant? Think of an example
it is scaled Both center and spread are impacted. Mean/ median/ stand dev/ iqr/ quartiles all multiplied by that constant. Center, spread and all individual values are changed. Consider 1,2,3,4,5 mean of 3 and range of 4. Now multiply by 3: 3,6,9,12,15 and you get a mean of 9 and a range of 12… both multiplied by three.
what is a z score?
the number of standard deviations away from the mean
what happens if you ADD a constant to each value in a data set?
it is SHIFTED only. Does not impact spread. This effects all of the data values and measures of center (mean, med) and quartiles, deciles, etc, IT DOES NOT CHANGE THE SPREAD! (IQR, St Dev, Range all stay the SAME).
Who chases the tail?
The mean chases the tail, the mean chases the tail, high-ho the derry-oh the mean chases the tail? and outliers??.
What is variability?
Differences, how things differ. There is variability everywhere. We all look different, act different, have different preference. Statisticians look at these differences.
If you want to calculate the probability (%) something falls between two values in a normal model, what do you do?
find z scores for both value, and then normcdf (Z LOW, Z HIGH )
What is meant by cumulative frequency?
ADD up the frequencies as you go. Suppose you are selling 25 pieces of candy. You sell 10 the first hour, 5 the second, 3 the third and 7 in the last hour, the cumulative frequency would be 10, 15, 18, 25
How do you find relative frequency?
just divide frequency by TOTAL. Make it a percent so it is relative to the whole.
What do we sometimes call a categorical variable?
qualitative
What is the IQR?
Interquartile range? a measure of spread. Q3-Q1. The distance from Q1 to Q3. The regular range is Hi-Lo, this is the inner range, the interquartile range.
What is a parameter?
A numerical summary of a population. Like a mean, median, range of a population
How can you match boxplots to histograms?
USE THE FISH TANK METHOD!
When can you round?
AT THE VERY END!!! (keep 3 digits until end!)
the output for normcdf(Zleft, Zright) is_______
the area under the normal curve between the given z scores
What is a standard deviation?
average distance to the mean (about)
For information purposes, which gives LEAST? stem-leaf, histogram or box-whisker?
Box/Whisker, BE CAREFUL. you really don’t know how things are distributed. The box and whisker and fish tank give a very GENERAL look.
What do you call things that are not independent?
associated. Or not independent. We generally don’t say DEPENDENT (unless talking about y variable on a scatterplot).
If you want to find % below a value, what do put into normcdf (? ?)
find z score for value, and then normcdf (-999, Zright)
What is the mode?
the most common, or the peaks of a histogram. We often use mode with categorical data.
What is Statistics?
The study of variability
How can you describe shape?
unimodal, bimodal, multimodal, uniform, symmetric, skewed
What is the difference between discrete and continuous variables?
Discrete can be counted, like “number of cars sold” they are generally integers (you wouldn’t sell 9.3 cars), while continuous would be something like weight of a mouse. 4.344 oz. Summaries of discreet variables will often be decimals.
What are the percentiles for Q1, med, and Q3?
25, 50 and 75
If asked to compare distributions, what should you write about?
Compare Shapes, Centers, Spreads, and Stranges. The GSOCS
What does normcdf do?
It gives you the area under the normal curve between any two z scores
What is meant by relative frequency?
The PERCENT of time something comes up (frequency/total)
How do students often mix up IQR and St. Dev
They INCORRECTLY think that Q1 is 1sd below the mean and Q3 is 1sd above the mean. THIS IS NOT TRUE!!! Q1 is only .67 sd above the mean and Q2 is .67 below
what are the percentiles from left to R on normal model?
2.5-16-50-84-97.5
What percentile is the median (aka Q2)?
50th
What percent of the data is between Q1 and Q3?
50%
What is the difference between quantitative and categorical data?
The data is the actual gathered measurements. So, if it is eye color, then the data would look like this “blue, brown, brown, brown, blue, green, blue, brown etc.” The data from categorical variables are usually words, often it is simpy “YES, YES, YES, NO, YES, NO” If it was weight, then the data would be quantitative like “125, 155, 223, 178, 222, etc.” The data from quantitative variables are numbers.
How many SD wide is the IQR in a normal distribution?
NOT 2!!!! Think about it. The middle 68% is 2 sd wide, since the IQR is only the middlest 50% it must be less than 2. try [invnorm(.75)] x2. You find that it is only 1.35 SD wide if the distribution is nearly normal.
what is a clear example of the medians resiliance and when you would use the median instead of the mean?
(change just the top value). Imagine if we asked eight people how much money they had in their wallet. We found they had {1, 2, 2, 5, 5, 8, 8, 9}. The mean of this set is 5, and the median is also 5. You might say “the average person in this group had 5 bucks.” But imagine the same group the next week, but one of them just got back from the casino and the dist was (1, 2, 2, 5, 5, 8, 8, 9000}, in this case, the median would still be 5, but the mean goes up to over 1000. Which number better describes the amount of money the average person in the group this time? 5 bucks or 1000 bucks? I think 5 is a better description of the average person in this group and the 9000 is simply an outlier.
If I take a random sample of 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and I do this because I want to know the true average number of pickles on a burger at FIVE GUYS, the true average number of pickles is considered a ______?
parameter, a one number summary of the population. The truth. AKA the parameter of interest.
If a distribution is skewed right, what will be greater, the mean or median? WHY?
Mean. The mean moves further to the right to keep balance.
If I take a random sample 20 hamburgers from FIVE GUYS and count the number of pickles on a bunch of them? and the average number of pickles was 9.5, then 9.5 is considered a _______?
statistic. It is a summary of a sample.
where are the “outlier fences?”
1.5 IQR above Q3 and 1.5 IQR below Q1. Just a rule of thumb.
What is the total area under the normal curve?
1 or 1.000
Does a census make sense?
A census is ok for small populations (like Mr. Nystrom’s students) but impossible if you want to survey “AVERAGE TREE HEIGHT IN THE US”
What is the median?
the middlest number, it splits area in half (always in the POSITION (n+1)/2 )
What does GSOCS stand for?
Gaps Shape Outliers Center Sprea
What is the mean?
the old average we used to calculate. It is the balancing point of the histogram
We are curious about the average wait time at a Dunkin Donuts drive through in your neighborhood. You randomly sample cars one afternoon and find the average wait time is 3.2 minutes. What is the population parameter? What is the statistic? What is the parameter of interest? What is the data?
The parameter is the true average wait time at that Dunkin Donuts. This is a number you don’t have and will never know. The statistic is “3.2 minutes.” It is the average of the data you collected. The parameter of interest is the same thing as the population parameter. In this case, it is the true average wait time of all cars. The data is the wait time of each individual car, so that would be like “3.8 min, 2.2 min, .8 min, 3 min”. You take that data and find the average, that average is called a “statistic,” and you use that to make an inference about the true population parameter.
What is categorical data?
The actual individual category from a subject, like “sedan” or “blue” or “female” or “sophomore”
Which calculator function gives you a z score?
invnorm(%ile)
How does multiplying by a constant impact the summary statistics of a data set? (or random variable)
It is SCALED. Both center and spread are effected. They all (mean, median, IQR, SD, range) get multiplied by three. (BE CAREFUL, remember the variance is the SD squared, so the variance gets multiplied by 9).
If you are tasting soup.. Then the flavor of each individual thing in the spoon is the _____, the contents of the entire spoon is a ______.. The flavor of all of that stuff together on the spoon is like the _____ and you use that to _____ about the flavor of the entire pot of soup, which would be the__________.
If you are tasting soup. Then the flavor of each individual thing in the spoon is DATA, the contents of the entire spoon is a SAMPLE. The flavor of all of that stuff together on the spoon is like the STATISTIC, and you use that to MAKE AN INFERENCE about the flavor of the entire pot of soup, which would be the PARAMETER. Notice you are interested in the parameter to begin with… that is why you took a sample.
For information purposes, which gives most? stem-leaf, histogram or box-whisker?
Stem leaf gives the actual values and the shape? histogram just the shape? and box-whisker the least amt, but are great for comparing multiple distributions.
Give an example of independent variables
If 80% prefer cheese and only 20% prefer pepperoni IN EACH GRADE AT BHS?then they all have the same preference, so grade doesn’t matter. We say “school year and pizza choice are independent”
What symbols do we use for population mean and sample mean?
Mu for population mean, xbar for sample mean.
Use the following words in one sentence: population, parameter, census, sample, data, statistics, inference, population of interest.
I was curious about a population parameter, but a census was too costly so I decided to choose a sample, collect some data, calculate a statistic and use that statistic to make an inference about the population parameter (aka the parameter of interest).
What is INFERENTIAL STATISTICS?
The part of the course where you look at your data and use that to say stuff about the BIG PICTURE. like tasting soup. a little sample can tell you a lot about the big pot of soup (the population)
What percent of the data is above Q3?
25%
What is quantitative data?
The actual numbers gathered from each subject. 211 pounds. 67 beats per minute.
What is the difference between a sample and a census?
With a sample, you get information from a small part of the population. In a census, you get info from the entire population. You can get a parameter from a census, but only a statistic from a sample.
What percent of the data is below the median?
50%
Compare population to sample
populations are generally large, and samples are small subsets of these population. We take samples to make inferences about populations. We use statistics to estimate parameters.
marginal distribution
distribution in the margins (outside of the table). The overall distributions of a single variable in contingency table.
Gender and Video Game playing are___________ because_______
associated (or not independent) because a higher percentage of males play video games. (think.. It depends on gender)
When do we often use mode?
With categorical variables. For instance, to describe the average teenagers preference, we often speak of what ?most? students chose, which is the mode. “the average teenager likes mexican food.” It is also tells the number of bumps in a histogram for quantitative data (unimodal, bimodal, etc?).
What is a census?
Like a sample of the entire population, you get information from every member of the population
Year in school (F,S,J,S) and Pizza Preference (pepperoni or cheese) are __________ because _______________
independent because all grades have similar preference distributions..
40% cheese, 30%pepperoni, 20% veggie 10% other
What is the difference between categorical VARIABLES and categorical DATA?
The Variable is the overall category. Like “EYE COLOR”. The data is the actual measurement from the subjects. Like “blue, brown, blue”
What is a frequency distribution?
A table, or a chart, that shows how often certain values or categories occur in a data set.
What is the five number summary?
min, Q1 , Q2(median), Q3 and max
How are mean, median and mode positioned in a skewed right histogram?
mode- median- mean (mean chases the tail)
How do you find percentiles and make a boxplot from OGIVE?
Go across till you hit the curve and then STRAIGHT DOWN!
How do you find Q1 and Q3?
Q1 is the median of the bottom half and Q3 is the median of the upper half (they are the 25th and 75th percentiles)
How can you describe the center of a distribution?
give the mean (balance), median (splits area in half), mode (peaks, if bimodal talk about both modes) or say “centered around ____”
What is the difference between quantitative and categorical variables?
Quantitative variables are numerical measures, like height and IQ. Categorical are categories, like eye color and music preference
Can numbers be CATEGORICAL?
sure. Zip codes, sports jersey numbers, telephone numbers, social security nunmbers, area codes? these are categorical.
What is frequency?
How often something comes up
What are random variables?
If you randomly choose people from a list, then any quality measured.. their hair color, height, weight can be considered random variables. Same thing with cars.. If you randomly pick them then any quality measured is a random variable.
Make a guess as to what relative cumulative frequency is?
It is the ADDED up PERCENTAGES.. An example is selling candy, 25 pieces sold overall, with 10 the first hour, 5 the second, 3 the third, and 7 the fourth hour, we’d take the cumulative frequencies, 10, 15, 18 and 25 and divide by the total giving cumulative percentages, .40, .60, .64, and 1.00. Relative cumulative frequencies always end at 100 percent.
what is the emperical rule?
mean 68-95-99.7 yeah!
are any populations actually normal?
no, nothing is normal, just normalish. The only normal thing is the model we use.
If the distribution is skewed (or outliers/not symmetric) what would you use for center and spread statistics?
Median (center) and IQR (spread)
If the distribution is bimodal or multimodal, what would you use for center and spread statistics?
Talk about each mode (center) and maybe use the range or IQR. You could also say “one group seems to go from __ to __ and the other from about __ to __”
which calculator function gives you a percent?
normcdf(Z left, Z right)
Compare DATA-STATISTIC-PARAMETER using QUANTITATIVE example
Data are individual measures, like how long a person can hold their breath: ?45 sec, 64 sec, 32 sec, 68 sec.? That is the raw data. Statistics and parameters are summaries like ?the average breath holding time in the sample was 52.4 seconds? and a parameter would be ?the average breath holding time in the population was 52.4 seconds?
What is the variance?
The average squared distance to the mean. Or the SD2 (It is the SD before you take the square root, so it is the stuff under the radical in the formula)
What is the difference between a parameter and a statistic?
BOTH ARE A SINGLE NUMBER SUMMARIZING A LARGER GROUP OF NUMBERS. But pppp parameters come from pppp populations, sss statistics come from ssss statistics.
What is a statistic?
A numerical summary of a sample. Like a mean, median, range of a sample.
What are 2 major branches of AP STATS?
Inferential and Descriptive
What is the difference between a population mean and a sample mean?
population mean is the mean of a population, it is a parameter, sample mean is a mean of a sample, so it is a statistic. We use sample statistics to make inferences about population parameters.
How do you match OGIVES to histograms?
RECTANGLE DROP!!
How are mean, median and mode positioned in a skewed left histogram?
goes in that order, mean median mode
What is a contingency table?
shows distributions across 2 variables like gender and music pref. AKA 2-way table
Association and Independence. How are they related?
Variables are either independent or associated. Meaning: if one impacts the other then we say there is an association. If not, Then they are independent.
Compare data to parameters
Data is each little bit of information collected from the subjects. They are the INDIVIDUAL little things we collect, like “5, 7, 9” . if we have all of the data from the population, then we can summarize it by finding the average and that would be called a parameter. (if we only had a sample then the summary is called a statistic)
mean/SD/median/IQR. How do I know which ones to use?
when unimodal and symmetric, mean and sd. If skewed or outliers? Median and IQR. If bimodal? Talk about the MODES
Which is more sensitive to outliers and skewed? Mean, median. Sd or IQR?
Mean and SD are most influenced by outliers. median and IQR are RESISTANT, RESILIENT, ROBUST!!
What percentile is Q1?
25th
How do you find the median fro man OGIVE?
go halfway up the y axis, then shoot across to the curve, then straight down. It’s at the 50th percentile (halfway up)
How do you find 5 number summary from OGIVE?
Split the y axis in half, then half the top and bottom (making quarters). Shoot out to the right from 0, .25, .50, .75 and 1.00 till you hit the ogive, then go straignt down. Those numbers on the x axis correspond to the 5 numbers.
If the distribution is unimodal and symmetric, what would you use for center and spread statistics?
Mean (center) and Standard Deviation (spread)
Give a quick example of associated variables
A higher percentage of boys play video games than girls so we say “gender and video game playing are associated” or “gender and video game playing are not independent”
What is a population?
(not necessarily people). the group of stuff you’re interested in. It could be “bags of potato chips..” Sometimes it?s big, like “all teenagers in the US” other times it is small, like “all AP Stats students in my school”
What are DESCRIPTIVE STATS?
Tell me what you got! Describe to me the data that you collected, use pictures or summaries like mean, median, range, etc
conditional distribution?
A distribution within the table, along only one row or one column? NOT IN THE MARGINS. You are given a condition.. Then read along that row or column.
What percentile is Q3?
75th
What is a random sample?
When you choose a sample by rolling dice, choosing names from a hat, or other TRULY RANDOM generated sample. Humans can’t really do this well without the help of a calculator, cards, dice, or slips of paper.
If you want to calculate % above a value, what do you put into normcdf(? ?)
find z score for value, and then normcdf (Z left, 999)
Compare Descriptive and Inferential STATS
Descriptive explains you about the data that you have, inference uses that data you have to try to say something about an entire population?.
When we say “the average teenager” are we talking about mean, median or mode?
It depends, if we are talking height, it might be the mean, if we are talking about parental income, we’d probably use the median, if we were talking about music preference, we’d probably use the mode to talk about the average teenager.
What symbols do we use for population proportion (%) and sample proportion (%)?
p for population and p-hat for sample
Why are there different standard deviation formulas for population and sample? Arent they the same thing?
Both equations are actually doing the same thing. They both attempt to calculate the true population proportion. When you have all of the data from the population you just divide by n and get the actual SD. BUT If you only have a sample then you are using that to make a guess (inference) at what the population standard deviation is.. What happens is that samples tend to have less spread so their SD underestimates the population, BUT, when you divide by n-1 instead of n, It gives you a better estimate of what the population standard deviation is.
